11. Continuous Sensors

• There are a number of defining properties of interest when considering sensors,

Accuracy: a sensor will statistically vary about an exact reading. If we take a statistical range for all readings (e.g., ±3 standard deviations) this will be a reasonable accuracy. Accuracy can also be given as a relative value (e.g. percentage)

Resolution: Typically used for systems that ‘step’ through readings. This is the smallest increment that the sensor can detect.

Repeatability: When a single sensor condition is made and repeated, there will be a small variation for that particular reading. This is the repeatability.

Range: Natural limits for the sensor

Dynamic Response: the frequency range for regular operation of the sensor. Typically sensors will have an upper operation frequency, occasionally there will be lower frequency limits.

Environmental: temperature and humidity limits exist for many sensors

Calibration: most sensors require some degree of calibration, and their readings may drift over time.

Cost

11.1 Input Issues

• Analog signals are more complicated to deal with than digital signals. This is primarily because electrical noise will degrade the quality of the signal quickly.

• To deal with this there are a number of measures to be taken,

shielding: shielding is used to reduce the effects of electromagnetic interference.

• A simple shielding example is shown below. A shielded cable has a metal sheath. This sheath needs to be connected to the measuring device to allow induced currents to be drained. This prevents electromagnetic waves to induce voltages in the signal wires.

• The common voltage for each analog signal may be the same but more often it is different. If the commons are tied together we have a single ended system. If each signal is given its own common the connections are double ended. Most analog input cards allow a choice between one or the other.

• Signals from transducers are normally small and cannot be directly input into an analog input. To make these signals more usable Signal Conditioners are used.

• Signal conditioners are normally amplifiers to increase the signal strength, but some will also change the signal (eg. conversion from current to voltage).

• An example of a simple single ended amplifier is given below,

• An example of a differential amplifier with a current input is given below. Note that Rc converts a current to a voltage.

• An example of a differential to single ended amplifier is given below.

• The circuit below can be used to amplify the output of a resistive device.

11.2 Sensor Types

• A list of physical properties, and sensors to measure them is given below,

11.3.1 Potentiometers

• A variable resistor is used to convert an angle or displacement to resistance/voltage.

• These give absolute position readings.

• Linear resistors are used for measuring linear displacement.

• The basic principle of operation is that a moving wiper (sensor input) moves a contact along a resistor. The ends of the resistor are connected to reference voltages. As the wiper moves the potentiometer acts as a voltage divider and produces a voltage proportional to position.

• rotational potentiometers are the most popular. These may be limited to a fixed range either less than 360, or some number of turns.

• Advantages include,

typically inexpensive

easy to use

very common in a variety of forms, resistances, etc.

• Disadvantages include,

limited accuracy (there are high cost solutions)

subject to mechanical wear

11.3.2 Encoders

• An incremental encoder will produce a set of output pulses, and a direction as it is rotated.

• The encoder contains an optical disk with fine windows etched into it. As the encoder shaft is rotated, the etched disk inside rotates. As it rotates various optical sensors are turned on and off.

• There are two basic types,

absolute: the same shaft position will always give the same position reading

relative/incremental: these just indicate movement, and they require that other circuits or programs be used to track position

• How the openings are etched onto the disk determine whether it is absolute or relative.

• In actual encoders there can be thousands of divisions per rotation.

• With an absolute encoder the output is a binary or gray code number.

• A quadrature pulse counter uses two pulses out of phase and deduces distance and direction.

11.3.3 Resolvers

• These use small magnetic coils to detect positions and behave much like relative encoders.

11.3.4 Problems

Problem 11.1 What is the resolution of an absolute optical encoder that has six tracks? nine tracks? twelve tracks?

Answer 11.1 360°/64steps, 360°/512seps, 360°/4096 steps

11.4 Linear Position

11.4.1 Potentiometers

• A variable resistor is used to convert a displacement to resistance/voltage.

• These give absolute position readings.

• The basic principle of operation is that a moving wiper (sensor input) moves a contact along a resistor. The ends of the resistor are connected to reference voltages. As the wiper moves the potentiometer acts as a voltage divider and produces a voltage proportional to position.

11.4.2 Linear Variable Differential Transformers (LVDT)

• This is effectively a transformer with a moving inner core. The moving core changes the inductance, and this can be converted to a position.

• In these devices there are three sets of windings. The first set of windings is in the center, and is powered by an AC source. The other two coils are at the opposite sides of the main coils. As the core is moved forward/back the magnetic coupling will change.

• If the core shown is in the center, the output will be 0Vac, as it shifts to the left there will be more coupling between the center and left coil, and the signal magnitude will be larger than the right hand coil. This difference can be converted to a calculated difference.

• This sensor is used for linear position sensing to high accuracies such as,

load cells

Bourdon tubes

dimensional measurement for SPC

bellows/diaphragm

• The signals from the LVDT can be conditioned with the circuit below.

• Near the center of the movement range the voltage is linearly proportional to core movement.

11.4.3 Moire Fringes

• By overlapping two fine lines patterns we can measure displacement.

• These are used in high precision applications, and are not available as off the shelf sensors.

11.4.4 Interferometers

• Uses the fact that when light is 180 degrees out of phase it cancels out.

• By finding the phase between outgoing and returning light (from lasers typically) the distance can be found.

11.5 Velocity

• This can be measured with dedicated sensors.

• We may also differential the output of a position sensor to find a velocity

11.5.1 Velocity Pickups

• Output voltage is proportional to velocity (V/(cm/s))

• These devices have low natural frequencies, and are used for signals with higher frequencies.

• well suited to measuring severe vibrations, but it may be affected by noise from AC sources.

• because signals are velocity, some form of integration must be done, making these devices bulky, and somewhat inaccurate

Stud mounted transducers have a thin layer of silicone grease to improve contact

11.5.2 Tachometers

• These devices measure the angular velocity of a rotating shaft.

• One way is to connect a DC generator (motor). The faster the shaft turns, the higher the voltage.

• Another technique uses a magnet with a pickup coil. As the magnet passes the coil a pulse is generated. The pulse magnitude and frequency are proportional to speed.

11.6 Acceleration

• Like velocity we may also find acceleration by differentiating velocity, or by differentiating position twice.

11.6.1 Accelerometers

Vibration Source: hammers can be used to generate impulse/step function responses. Load cells/vibrators can be used to excite frequency responses (Bode plots and phase shift plots)

Sensors: Velocity Pickups/Accelerometers: lightweight devices that are mounted on structures. They produce small voltages (approx. 10mV). Velocity meters are not as accurate as accelerometers. Accelerometers are very common, and are used for vibrations above 1KHz. Many other sensors are possible.

Preamplifiers: Can power sensors, filter and amplify output.

Signal Processor: Many types used, from software packages, to older pen based plotters, or tape recorders

• Compared to velocity pickups

smaller

more sensitive

wider frequency range

• electronic integrators can provide velocity and position

• The accelerometer is mounted with electrically isolated studs and washers, so that the sensor may be grounded at the amplifier to reduce electrical noise.

• Cables are fixed to the surface of the object close to the accelerometer, and are fixed to the surface as often as possible to prevent noise from the cable striking the surface.

• Background vibrations in factories are measured by attaching control electrodes to ‘non-vibrating’ surfaces. (The control vibrations should be less than 1/3 of the signal for the error to be less than 12%)

• Piezoelectric accelerometers typically have parameters such as,

-100to250°C operating range

1mV/g to 30V/g

operate well below one forth of the natural frequency

• Accelerometer designs vary, so the manufacturers specifications should be followed during application.

• There is often a trade-off between wide frequency range and device sensitivity (high sensitivity requires greater mass)

• Two type of accelerometers are compression and shear types.

• Mass of the accelerometers should be less than a tenth of the measurement mass.

• Accelerometers can be linear up to 50,000 to 100,000 m/s**2 or up to 1,000,000 m/s**2 for high shock designs.

• Typically used for 10-10,000 Hz, but can be used up to 10KHz

• Temperature variations can reduce the accuracy of the sensors.

• typical parameters are,

• These devices can be calibrated with shakers, for example a 1g shaker will hit a peak velocity of 9.81 m/s**2

11.7 Forces and Moments

• These values cannot currently be measured directly, and count on indirect measurements based on deflections or strain.

11.7.1 Strain Gages

• These devices are attached to surfaces. As the surfaces experience stress/strain the devices are stretched and the resistance changes.

• The basic theory is based on a stretched wire.

• Changes in strain gauge values are typically small (large values would require strains that would cause the gages to plastically deform). As a result the resistance values are also small, so we can use resistor bridges (eg whetstone bridge) to amplify the effect. In this circuit the variable resistor R2 should be turned until the circuit is balanced for no strain.

• If the strain gauge is placed in the direction of the strain it will read the full strain. If the gauge is perpendicular, the reading will be zero.

uniaxial: the direction is critical

rosette: two gages at 90deg. to each other will measure strain components in two direction (and can measure shear).

• In some machines (etc.) a strain gauge is often mounted on a narrowed member to measure force. This is typically known as a load cell.

• Strain gages are normally made on thin films that are attached (mounted) to surfaces through a process that involves surface preparation and attachment with adhesives.

11.7.2 Piezoelectric

• These are ceramic and crystal materials that will generate a small amount of charge when deformed (the capacitance also changes).

• If the deformation is linear,

11.8 Flow Rate

• Fluid flow rate is important for a number of processes such as cooling and chemical.

11.8.1 Venturi

• A Venturi valve uses a narrow section of a pipe to generate a pressure differential from the normal pipe diameter. The pressure differential will increase with the velocity of the flow. By measuring the pressure we can determine the flow rate.

Problem 11.3 If a thermocouple generates a voltage of 30mV at 800F and 40mV at 100F, what voltage will be generated at 1200F?

Problem 11.4 A certain potentiometer is to be used as the feedback device to indicate position of the output link of a rotational robot joint. The excitation voltage of the potentiometer equals 5.0 V, and the total wiper travel of the potentiometer is 300 degrees. The wiper arm is directly connected to the rotational joint so that a given rotation of the joint corresponds to an equal rotation of the wiper arm.

a) Determine the voltage constant of the potentiometer Kp,

b) The robot joint is actuated to a certain angle, causing the wiper position to be 38 degrees. Determine the resulting output voltage of the potentiometer.

c) In another actuation of the joint, the resulting output voltage of the potentiometer is 3.75V. Determine the corresponding angular position of the output link.

Problem 11.5 How is the efficiency of a motor defined?

Problem 11.6 What is the relationship between Real Power, Reactive Power and Apparent Power? (A sketch is acceptable)

Problem 11.7 What is the definition of the power factor of a motor?

Problem 11.8 Name two ways to improve motor efficiency.

Problem 11.9 Name two types of inputs that would be analog input values (versus a digital value).

Problem 11.10 Describe the following as either Transient or Steady State problems with respect to Power Quality: